Various methods have been developed for solving SAT problems, notably resolution, the Davis-Putnam-Logemann-Loveland-Procedure procedure (DPLL) and an extension of it, the conflict-driven clause learning (CDCL). We have formalised these three algorithms in a proof assistant Isabelle/HOL, based on a chapter of Christoph Weidenbach’s upcoming book Automed Reasoning – The Art of Generic Problem So...

Satisfiability solvers that are based on the Davis-Putnam-Logemann-Loveland (DPLL) algorithm operate on propositional logic formulas in conjunctive normal form (CNF). Despite major improvements in solver technology, using only CNF does not seem to scale well for problem instances involving XOR expressions. We present a decision procedure to determine effectively the satisfiability of XOR clause...

The DPLL procedure for the SAT problem is one of the fundamental algorithms in computer science, with many applications in a range of domains, including software and hardware verification. Most of the modern SAT solvers are based on this procedure, extending it with different heuristics. In this paper we present a formal proof that the DPLL procedure is correct. As far as we know, this is the f...

This paper discusses an NP-complete constraint satisfaction problem which appears to share many of the threshold characteristics of SAT but is similar to XOR-SAT and so is easier to analyze. For example, the exact satisfiability threshold for this problem is known, and the problem has high resolution complexity. In this paper, we prove the problem appears hard for DPLL. Specifically, if we pick...

Satisfiability solving is the problem of determining whether a given formula has a solution. The most ubiquitous and well-studied satisfiability problem is propositional satisfiability (SAT), in which all variables are Boolean. In recent years, the field of satisfiability modulo theories (SMT) has extended methods in SAT solving to accommodate existential first order formulas with non-Boolean v...

We present a novel low-overhead framework for encoding and utilizing structural symmetry in propositional satisfiability algorithms (SAT solvers). We use the notion of complete multi-class symmetry and demonstrate the efficacy of our technique through a solver SymChaff that achieves exponential speedup by using simple tags in the specification of problems from both theory and practice. Efficien...

This paper presents a DCO dithering technique which employs a finer fractional gain control to suppress nonlinear effect of a bang-bang digital PLL (BB-DPLL).

We study the performance of DPLL algorithms on parameterized problems. In particular, we investigate how difficult it is to decide whether small solutions exist for satisfiability and other combinatorial problems. For this purpose we develop a Prover-Delayer game which models the running time of DPLL procedures and we establish an information-theoretic method to obtain lower bounds to the runni...

DPLL Modulo Theories Works with any DPLL engine and T -solver but is best with 1. an on-line DPLL engine and 2. an incremental T -solver Tableaux 2007 – p.29/40 Abstract DPLL Modulo TheoriesDPLL Modulo Theories Works with any DPLL engine and T -solver but is best with 1. an on-line DPLL engine and 2. an incremental T -solver It consists of the following rules: Propagate, Decide, Fail, Restart (...